Parametric topological entropy of families of multivalued maps in topological spaces and induced hyperspace maps

Abstract

A positive parametric topological entropy is examined whether or not it is preserved from given continuous maps to the induced hyperspace maps. An established affirmative answer generalizes all the related results obtained in this field so far, because the continuous maps under consideration can be multivalued and nonautonomous (time-dependent) in compact topological Hausdorff spaces. A variety of definitions of parametric topological entropy for multivalued maps is investigated, together with their properties. Several simple illustrative examples are supplied.